A car starts moving rectilinearly first with acceleration $ a= 5 m/s^2$( the initial velocity is equal to zero ) then uniformly and finally be decelerating at the same rate$ a$ and comes to stop. The total time of the motion equal to $25 s $ the average velocity during that time is equal to 72 km/h . How long does the car move uniformly ?

I tried this by thinking that if car has constant acceleration first then its average velocity would have been same throughout the middle journey where it has uniform velocity and that is 20 m/s
so if it takes 4 seconds to accelerate and decelerate then 25 -8 = 17 sec

1 Answer

1 vote

Best answer

The average speed over the whole journey is 20 m/s so the total distance covered is 20 x 25 = 500 m.

Suppose the acceleration phase lasts time t. Then the maximum speed is v=5t. The total distance covered is the area of the trapezium with parallel sides of 25 and 25-2t separated by distance v. So
$\frac12 v(25+25-2t)=5t(25-t)=500$
$t(25-t)=100$.

By inspection t=5 s. So the time spent at maximum speed is 25-2t = 15 s.